In this and the next lesson, students discover that the values of the sine and cosine ratios in a right triangle depend solely on the measure of the acute angle by which the adjacent, opposite, and hypotenuse sides are identified. To do this, students first learn how to identify these reference labels. Then, two groups take measurements and make calculations of the values of the and ratios for two sets of triangles, where each triangle in one set is similar to a triangle in the other. This exploration leads to the conclusion regarding the “incredibly useful ratios.”

In geometry, sine, cosine, and tangent are thought of as the value of ratios of triangles, not as functions. No attempt is made to describe the trigonometric ratios as functions of the real number line. Therefore, the notation is just an abbreviation for the “sine of an angle” ( ) or “sine of an angle measure” ( ). Parentheses are used more for grouping and clarity reasons than as symbols used to represent a function.

What if you were given a right triangle and told that its sides measure 3, 4, and 5 inches? How could you find the sine, cosine, and tangent of one of the triangle's non-right angles? After completing this Concept, you'll be able to solve for these trigonometric ratios.

Lessons, videos, exercises, and text from CK-12. Additional resources available at this site.